The 19-year-old had only just returned to international cricket after missing the whole of Australia's summer after suffering a foot injury against South Africa in November.
Cummins, who made his return after the lengthy absence last Sunday in an ODI against Ireland, will leave for home on Monday.
"Pat sustained an abdominal muscle strain on his left side during the first ODI at Lord's," Australian team doctor John Orchard said.
"Whilst he was able to complete his 10 overs, he was sore after the game and was scanned, the results of which have revealed a medium grade side-strain.
"This will keep him out of the remainder of the England tour. His return to cricket will be decided in due course, based on follow-up examinations in Australia."
Australia will not name a replacement for Cummins as they have enough pacemen in the ODI squad, the statement added.
Hosts England defeated Australia by 15 runs in the first of the five matches in the series.
England fast bowler James Anderson was ruled out of the second match on Sunday because of a groin injury.
Anderson, troubled by a 'tight groin' in Friday's victory at Lord's, was replaced at the Oval by Jade Dernbach - the only change to England's winning team.